This preview shows pages 1–3. Sign up to view the full content.
Problem 7.15 in SPF
EEL 3135: Signals and Systems
G. Heitman
Electrical and Computer Engineering
University of Florida
Spring 2006
fs
1000
:=
Ts
1
fs
:=
gcd 750 2000
,
(
)
250
=
Hence the fundamental freq. and period of the CT signal are
f0
125
3
:=
T0
1
f0
:=
T0
0.024
=
The input contains dc and the 3
rd
and 8
th
harmonics
x
ct
t
( )
4
cos 2
π
⋅
3f0
⋅
()
⋅
t
⋅
π
4
−
⎡
⎣
⎤
⎦
+
3 cos 2
π
⋅
8f0
⋅
⋅
t
⋅
⎣
⎦
⋅
−
:=
The given CT input
x
dt
n
x
ct
nTs
⋅
:=
The ideally sampled signal.
Its fundamental period is
N0
T0
Ts
:=
N0
24
=
Fortunately the problem is set up
so that T0/Ts is an integer
The fundamental freq. of the DT input:
ω
0
2
π
⋅
N0
:=
ω
0
1
12
π
⋅
→
The DT signal contains dc and the 3
rd
and 8
th
harmonics:
3
ω
0
⋅
1
4
π
⋅
→
8
ω
0
⋅
2
3
π
⋅
→
tmin
0
:=
tmax
2 T0
⋅
:=
ε
tmax
tmin
−
1000
:=
t
tmin tmin
ε
+
,
tmax
..
:=
n0
2
N
0
⋅
..
:=
EEL 3135
1
P7.15.mcd
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document0
0.01
0.02
0.03
0.04
0.05
5
10
The CT Input and Its Samples
4
x
ct
t
()
x
ct
nTs
⋅
T0
tnT
s
⋅
,
01
02
03
04
05
0
5
10
The DT Input
4
x
dt
n
N0
n
The DT system function:
H
z
1
3
1z
1
−
+
z
2
−
+
⋅
:=
The DT output signal:
y
dt
n
( )
4 H exp i 0
⋅
⋅
H exp i 3
⋅ω
0
⋅
cos 3
ω
0
⋅
n
⋅
π
4
−
arg H exp i 3
0
⋅
+
⎛
⎝
⎞
⎠
⋅
+
3
−
(
)
H exp i 8
0
⋅
⋅
cos 8
ω
0
⋅
n
⋅
arg H exp i 8
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 ?

Click to edit the document details